One way some of us even out the morale/approval of our empire is to move the population off of one planet to another. If your homeworld is overpopulated, you can use a colonizer or transport to move the people from there to an underpopulated planet. Sometimes, having an even population distribution can make it easier to manage empire wide approval.
As mentioned above by Piznit, researching the morale techs can get you ahead there. Also, grab a morale resource or two, if you can. Add modules to it as your tech allows. The better your morale, the higher you can set your tax rate.
Make sure you don't build too many farms. They will add to your overpopulation problems. Populations of 20b or under are manageable. 13b is real easy.
If you'd like, visit the
Tyranny of Evil Forums and poke around for hints and tips there. You can even just visit as a guest and pick up quite a few tips.
Joining a team on the
Metaverse League can also be a good source of ideas. You'd be welcome there as a new player or veteran. All are equally welcome.